## The Annals of Mathematical Statistics

### Consistency and Unbiasedness of Certain Nonparametric Tests

E. L. Lehmann

#### Abstract

It is shown that there exist strictly unbiased and consistent tests for the univariate and multivariate two- and $k$-sample problem, for the hypothesis of independence, and for the hypothesis of symmetry with respect to a given point. Certain new tests for the univariate two-sample problem are discussed. The large sample power of these tests and of the Mann-Whitney test are obtained by means of a theorem of Hoeffding. There is a discussion of the problem of tied observations.

#### Article information

Source
Ann. Math. Statist., Volume 22, Number 2 (1951), 165-179.

Dates
First available in Project Euclid: 28 April 2007

https://projecteuclid.org/euclid.aoms/1177729639

Digital Object Identifier
doi:10.1214/aoms/1177729639

Mathematical Reviews number (MathSciNet)
MR40632

Zentralblatt MATH identifier
0045.40903

JSTOR